A forced pendulum equation with many periodic solutions
type: Item
instance of: scholarly article
title: A forced pendulum equation with many periodic solutions
zbMATH Open document ID: 0899.34031
author: Rafael Ortega
published in: Rocky Mountain Journal of Mathematics
publication date: 1998-11-15T00:00:00Z
full work available at URL: CONT27-3.html
review text: The author shows that if \(a\) is a positive real number and \(n\) an integer greater than or equal to \(1\), then there exists \(p(t)\) satisfying \(p\in L^1(\mathbb{R}/T\mathbb{Z})\), and \(\int^T_0 p(t)dt= 0\), such that the forced pendulum equation \(x''+ a\sin x= p(t)\) has at least \(2n\) \(T\)-periodic solutions which are geometrically different.
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1143478
zbMATH Keywords: periodic solutions
zbMATH Keywords: bifurcation
zbMATH Keywords: forced pendulum equation
reviewed by: Olusola Akinyele
MaRDI profile type: Publication
OpenAlex ID: W2019862730
cites work: Reduction Theorems for a Class of Semilinear Equations at Resonance
cites work: Q3292729
cites work: Q4272493
cites work: Periodic solutions of 𝑥”+𝑐𝑥’+𝑔(𝑥)=𝜖𝑓(𝑡)
cites work: The forced pendulum: A paradigm for nonlinear analysis and dynamical systems
DOI: 10.1216/RMJM/1181071898
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description: scientific article; zbMATH DE number 1143478